Existence Of Solutions For Time Research Articles

Blowup in L 1(Ω)-norm and global existence for time-fractional diffusion equations with polynomial semilinear terms

Abstract This article is concerned with semilinear time-fractional diffusion equations with polynomial nonlinearity u p {u}^{p} in a bounded domain Ω \Omega with the homogeneous Neumann boundary condition and positive initial values. In the case of p > 1 p\gt 1 , we prove the blowup of solutions u ( x , t ) u\left(x,t) in the sense that ‖ u ( ⋅ , t ) ‖ L 1 ( Ω ) \Vert u\left(\hspace{0.33em}\cdot \hspace{0.33em},t){\Vert }_{{L}^{1}\left(\Omega )} tends to ∞ \infty as t t approaches some value, by using a comparison principle for the corresponding ordinary differential equations and constructing special lower solutions. Moreover, we provide an upper bound for the blowup time. In the case of 0 < p < 1 0\lt p\lt 1 , we establish the global existence of solutions in time based on the Schauder fixed-point theorem.

Existence of Solutions for Time Second Order Nonmonotone Differential Equations Involving Convex Potentials with Periodic and Anti-periodic Boundary Conditions

Existence of Solutions for Time Second Order Nonmonotone Differential Equations Involving Convex Potentials with Periodic and Anti-periodic Boundary Conditions

SOLUÇÃO PARA AS EQUAÇÕES DE NAVIER-STOKES EM DOMÍNIOS TRIDIMENSIONAIS FINOS

The classical form of the Navier-Stokes equations system, which is derived from the principle of conservation of mass and momentum, describes the motion of a homogeneous fluid subject to a field of external forces. In this work, we develop a study to find the maximal interval of existence of solutions in time to the Navier-Stokes equations in a three dimensional thin domain, i.e., Ω = ω × (0, ∈), where ω ⊂ R² e ∈ ∈ (0, 1), considering different combinations of boundary conditions.

The Global Existence of Solutions in Time for a Chemotaxis Model with Two Chemicals

This paper concerns the uniform boundedness and global existence of solutions in time for the chemotaxis model with two chemicals. We prove the system has global existence of solutions in time for any dimensionn.

The Existence of a Global Attractor for the S-K-T Competition Model with Self-Diffusion

This paper concerns the uniform bounds of the global existence of solutions in time for the S-K-T competition model with self-diffusion. We prove that the system has a global attractor forn<8.

Time-periodic solutions of the time-dependent Ginzburg-Landau equations of superconductivity

The problem of existence of time-periodic solutions for the time-dependent Ginzburg-Landau equations of superconductivity is discussed. It is assumed that the applied magnetic field H is τ-periodic in time, and so is the associated dynamical process. We prove the existence of τ-periodic solutions in time, which are exactly the fixed points of the associated period mapping.